Nick Clegg has accused David Cameron of being "stuck in the past" for opposing a mansion tax, amid signs that the Liberal Democrats are ready to challenge the Tories more vigorously over key aspects of economic policy.

Writing in the Observer ahead of Thursday's crucial Eastleigh byelection, Clegg attacks Cameron and his party for being instinctively against fairer taxation "even as people on lower incomes feel the pinch".

The Lib Dem leader says plans for a mansion tax on properties worth more than £2m, recently backed by Labour, is an idea "whose time has come" and says it is a "certainty" that some levy on high-value properties will be introduced soon. "The Conservatives and opponents of fairer taxes have a choice," Clegg writes. "They can dig their heels in and remain stuck in the past. Or they can join with the Liberal Democrats and the chorus of voices seeking to make our tax system fair. Far better, surely, to move with the times."

His remarks come as further details emerge of allegations that one of his party's leading peers, Lord Rennard, abused his position to make sexual advances towards several women. An exchange posted on Facebook four years ago suggested that Clegg had been made aware of the complaints. One read: "I just don't know how Nick can know and not do anything." Sources have strongly denied that he knew of the allegations before they were brought to his attention by Channel 4.

Clegg's attack on Cameron comes after the announcement on Friday that the ratings agency Moody's was stripping Britain of its AAA-rated credit status – a move Labour's Ed Balls described as a humiliation for Cameron and George Osborne. While the Lib Dems remain committed to slashing the deficit through austerity cuts, Clegg's remarks will be viewed as evidence of a growing assertiveness over taxation as the party seeks to bolster its reputation for promoting fairness for low earners.

Hinting that the Lib Dems may be prepared to work with Labour on a mansion tax, Clegg adds: "As we try to build a stronger, more entrepreneurial economy who can possibly defend a tax system that rewards unearned wealth at the expense of hard work?" Balls said the loss of the AAA rating had left the government's economic policy in tatters. "This downgrade is a humiliating blow to a prime minister and chancellor who said keeping our AAA rating was the test of their economic credibility," he said.

Osborne, who is under increasing pressure from within the coalition to boost growth, described the downgrade as a "stark reminder of the debt problems facing our country" and argued that the outlook would be far worse if the government were to abandon its "commitment to deal with the debt problem". Danny Alexander, the Lib Dem chief secretary to the Treasury, said that the downgrade was "disappointing news", but that the UK's economic credibility stood up to scrutiny daily on the financial markets. Vince Cable, the Lib Dem business secretary, is known to be agitating for more capital spending to counterbalance the effects of austerity cuts.

A new Opinium/Observer poll conducted before the downgrade shows that more people still blame the last Labour government for the state of the economy (43%) than blame the coalition (34%). But the gap has narrowed since September when just 29% blamed the coalition most and 46% Labour. The poll puts Labour up 2% on 42%, compared to a fortnight ago, with the Tories unchanged on 29%, Ukip down 1% on 13%, and the Lib Dems unchanged on 8%.

Following Moody's decision, the pound fell to a two-year low against the dollar, at $1.5163, prompting fears of further fuel price rises. Because oil is traded in dollars, economists predict a 2%-3% increase in petrol prices over the next few months. But analysts said the downgrade would have little additional impact on government's borrowing costs. David Tinsley, an economist at the investment bank BNP Paribas, said: "The market had already expected a downgrade. We were probably already feeling the negative effects. One way that has been manifest is the cost of borrowing has risen over the last couple of months." Howard Archer, an economist at IHS Global Insight, said: "The negative impact for the UK is likely to be limited by the fact that there are now very few countries left that have an AAA rating from all of the credit rating agencies."

Moody's has put the UK rating on a "stable footing", and rival ratings agencies Fitch and Standard & Poor's have Britain under review for a potential downgrade. Fitch is expected to jump first, with economists predicting it will make a downgrade less than two weeks after the March budget.

Standard & Poor's might wait longer, being the last to put the rating under review. Tinsley said: "They might not look at it for a while yet, but there is a certain amount of momentum that builds on these things. It's possible they will come later this year."